INVENTORY CONTROL MANAGEMENT

OPERATIONS MANAGEMENT• OPERATIONS MANAGEMENT IS THE MANAGEMENT OF AN

ORGANIZATION’S PRODUCTIVE RESOURCES OR ITS PRODUCTION SYSTEM, WHICH CONVERTS INPUTS INTO THE ORGANIZATION’S PRODUCTS AND SERVICES.

• HISTORICAL MILESTONES IN OM:-

• THE INDUSTRIAL REVOLUTION• POST CIVIL WAR PERIOD• SCIENTIFIC MANAGEMENT• HUMAN RELATIONS AND BEHAVIOURALISM• OPERATIONS RESEARCH• THE SERVICE RESOLUTION• THE COMPUTER REVOLUTION

OPERATIONS RESEARCH• OPERATIONS RESEARCH SEEKS TO REPLACE INTUITIVE

DECISION MAKING FOR LARGE COMPLEX PROBLEMS WITH AN APPROACH THAT IDENTIFIES THE OPTIMAL OR BEST, ALTERNATIVE THROUGH ANALYSIS.

• CHARACTERISTICS OF OPERATIONS RESEARCH

• 1. INTER- DISCIPLINARY TEAM APPROACH• 2. WHOLISTIC APPROACH TO THE SYSTEM• 3. METHODOLOGICAL APPROACH• 4.OBEJECTIVISTIC APPROACH

THE OR APPROACH TO PROBLEM SOLVING CONSISTS OF THE FOLLOWING STEPS.

• 1. FORMULATE THE PROBLEM.• 2.DETERMINE THE ASSUMPTIONS ( MODEL BUILDING) AND

FORMULATE THE PROBLEM IN A MATHEMATICAL FRAMEWORK.• 3. ACQUIRE THE INPUT DATA• 4. SOLVE THE MODEL FORMULATED AND INTERPRET THE RESULTS.• 5. VALIDATE THE MODEL.• 6. IMPLEMENT THE SOLUTION OBTAINED.

• HOWEVER, ONE STEP NEED NOT BE COMPLATED FULLY BEFORE THE NEXT IS STARTED. IN FACT, ONE OR MORE OF THE STEPS MAY BE MODIDFIED TO SOME EXTENT BEFORE FINAL RESULTS ARE IMPLEMENTED.

• MATERIALS MANAGEMENT• MOST MANUFACTURING CONCERNS SPEND MORE THAN 60% OF THE MONEY THEY TAKE IN,

FOR MATERIALS; i.e. MATERIALS SOAK UP A SUBSTANTIAL PORTION OF THE CAPITAL INVESTED IN AN INDUSTRIAL CONCERN. THIS EMPHASIZES THE NEED FOR ADEQUATE MATERIALS MANAGEMENT AND CONTROL BECAUSE EVEN A SMALL SAVING IN MATERAILS CAN REDUCE THE PRODUCTION COST TO A FAIR EXTENT AND THUS ADD TO THE PROFITS.

• MATERIALS MANAGEMENT CAN BE THOUGHT OF AS AN INTEGRATED FUNCTIONING OF THE DIFFERENT SECTIONS OF A COMPANY DEALING WITH SUPPLY OF MATERIALS AND OTHER RELATED ACTIVITIES SO AS TO OBTAIN MAXIMUM CO-ORDINATION AND OPTIMUM MINIMUM EXPENDITURE ON MATERIALS.

• OBJECTIVES OF MATERIALS MANAGEMENT:-• TO MINIMIZE MATERIALS COST.• TO PROCURE AND PROVIDE MATERIALS OF DESIRED QUALITY WHEN REQUIRED, AT THE

LOWEST POSSIBLE OVERALL COST OF THE CONCERN.• TO REDUCE INVESTMENT TIED IN INVENTORIES FOR USE IN OTHER PRODUCTIVE PURPOSE AND

TO DEVELOP HIGH INVENTORY TURNOVER RATIOS.• TO PURCHASE, RECEIVE,TRANSPORT AND STORE MATERIALS EFFECIENTLY AND TO REDUCE THE

RELATED COST.• TO CUT DOWN COSTS THROUGH SIMPLIFICATION, STANDARDIZATION, CODIFICATION, VALUE

ANALYSIS.

• STANDARDIZATION & CODIFICATION• CONFUSION IN LOCATING THE MATERIALS LYING IN STORE LEADS TO AVOIDABLE DELAYS,

REDUCING THE VERY CONCEPT OF A STORING SYSTEM TO A FARCE. TO AVOID THIS, EACH MATERIAL OR ITEMS IN THE STORES SHOULD BE CLEARLY IDENTIFIED SO THAT THE SAME CAN BE EASILY LOCATED AT THE TIME OF NEED. THIS IS ACHIEVED BY ALLOCATING CODE NUMBERS.

• THE CODE SHOULD BE MEANINGFUL AND IMPART A UNIQUE IDENTITY TO EACH MATERIAL. IF A MATERIAL IS DESCRIBED BY ITS TRADE NAME, AS WELL AS BY A SERIAL NO. AND ALSO BY ITS FUNCTION, IT IS QUITE LIKELY THAT DIFFERENT QUANTITIES OF THE SAME MATERIAL MIGHT BE LOCATED AT THREE DIFFERENT LOCATIONS IN THE SAME STORE.THIS INCREASES SIZE OF THE INVENTORY AND CREATES AN UNNECESSARY CONFUSION. CODIFIACTION OF MATERAIALS REMOVES THIS DIFFICULTY AND AVOIDS DUPLICATION OF MATERIALS.

• CODIFICATION IS THE PROCESS OF REPRESENTING EACH ITEM BY A NUMBER OR ALPHABET, THE DIGITS OF WHICH INDICATE THE GROUP, THE SUB- GROUP, THE TYPE AND THE DIMENSION OF THE ITEM. SOME TIMES THE BIN LOCATION AND THE SUPPLIER’S NAME ARE ALSO INCLUDED IN THE CODIFICATION PROCESS.

• STANDARDIZATION MEANS PRODUCING MAXIMUM VARIETY OF PRODUCTS FROM THE MINIMUM VARIETY OF MATERIALS, PARTS,TOOLS AND PROCESSES. THE BENEFITS OF IT WOULD BE REDUCTION IN COST DUE TO THE USE OF STANDARD ITEMS,INCREASED EFFECIENCY IN PURCHASING AND SUBCONTRACTING OPERATIONS, INCREASED PRODUCTIVITY DUE TO LESS REJECTIONS,REDUCED INVENTORY LEVELS,EASY IDENTIFICATION ETC.

• INVENTORY MANAGEMENT• AN INVENTORY MAY BE DEFINED AS A STOCK OF IDLE RESOURCES OF ANY KIND HAVING AN

ECONOMIC VALUE.• INVENTORIES ARE VITAL TO THE SUCESSSFUL FUNCTIONING OF MANUFACTURING AND RETAILING

ORGANIZATIONS. THE INVENTORIES MAY CONSIST OF RAW MATERIALS,WORK-IN-PROGESS, SPARE PARTS/CONSUMABLES, FINISHED GOODS, HUMAN RESOURCE SUCH AS UNUSED LABOUR OR FINANCIAL RESOURCE SUCH AS WORKING CAPITAL ETC.

• THERE ARE MANY REASONS WHY WE LIKE TO HAVE INVENTORIES, BUT THERE ARE ALSO REASONS WHY HOLDING INVENTORIES IS CONSIDERED TO BE UNWISE.

• WHY DO WE WANT TO HOLD INVENTORIES?

• FINISHED GOODS :• 1. ESSENTAIL IN PRODUCE TO STOCK POSITIONING STRATEGIES, OF STRATEGIC IMPORTANCE.• 2. PRODUCTS CAN BE DISPLAYED TO CUSTOMERS.• IN PROCESS:• 1. NECESSARY IN PROCESS-FOCUSED PRODUCTION, UNCOUPLES THE STAGES OF

PRODUCTION;INCREASES FLEXIBILITY.• 2.PRODUCING AND TRANSPORTING LARGER BATCHES OF PRODUCTS CREATES MORE INVENTORY BUT

MAY REDUCE MATERILAS-HANDLING AND PRODUCTION COSTS.• RAW MATERIALS:• 1. SUPPLIERS PRODUCE AND SHIP SOME RAW MATERIALS IN BATCHES.• 2. LARGER PURCHASES RESULT IN MORE INVENTORY, BUT QUANTITY DISCOUNTS AND REDUCE

FRIEGHT AND MATERILA HANDLING COST MAY RESULT.

• HOWEVER CERTAIN COSTS INCREASE WITH HIGHER LEVEL OF INVENTORIES LIKE CARRYING COST, COST OF DILUTED RETURN ON INVESTMENT.

• THUS, THE PROBLEM IS TO BALANCE BETWEEN THE ADVANTAGE OF HAVING INVENTORIES (OR LOSSES THAT MAY BE EXPECTED FROM NOT HAVING ADEQUATE INVENTORIES) AND COST OF CARRYING THEM TO ARRIVE AT AN OPTIMAL LEVEL OF INVENTORIES TO MINIMIZE THE TOTAL INVENTORY COST.

• PUTTING IT IN ANOTHER WORDS, WE CAN STATE THAT THAT THE BASIC OBJECTIVE OF INVENTORY CONTROL IS TO RELAESE CAPITAL FOR MORE PRODUCTIVE USE. INVENTORIES SHOULD BE ADEQUATE ENOUGH TO ACHIEVE MAXIMUM PRODUCTION AND SALES. AT THE SAME TIME IT SHOULD NOT BE SO EXCESSIVE AS TO RESTRICT THE ABILITY OF AN ORGANIZATION TO EARN HIGH RATE OF RETURN.

• TYPES OF INVENTORIES:-• 1. SAFETY OR BUFFER INVENTORIES : THESE HAVE TO BE CARRIED BECAUSE SALES AND

PRODUCTION TIMES FOR THE PRODUCT CAN NOT ALWAYS BE PREDICTED ACCURATELY. THERE ARE FLUCTUATIONS IN DEMAND AND LEAD-TIMES REQUIRED TO MANUFACTURE ITEMS.

• 2. LOT –SIZE (OR CYCLE ) INVENTORIES: IN MANY CASES, PRODUCTION AND MATERIAL PROCUREMENT TAKE PLACE IN BATCHES. THIS RESULT IN LOT-SIZE INVENTORY.

• 3. SEASONAL OR ANTICAIPATION INVENTORY: ANTICIPATION INVENTORIES ARE BUILT UP IN ADVANCE FOR A BIG SELLING SEASON, A PROMOTION PROGRAMME OR APLANT SHUT- DOWN PERIOD.

• 4. PROCESS OR PIPE LINE INVENTORIES: THIS CONSISTS OF MATERIALS ACTUALLY BEING WORKED ON, OR MOVING BETWEEN WORK CENTRES, OR BEING IN TRANSIT TO DISTRIBUTION CENTRES AND CUSTOMERS.

• 5. DECOUPLING INVENTORIES: THESE ARE THOSE TYPE OF INVENTORIES USED TO REDUCE THE INTERDEPENDENCE OF VARIOUS STAGES OF THE PRODUCTION SYSTEM.

STRUCTURE OF INVENTORY MANAGEMENT SYSTEM AN INVENTORY SYSTEM CAN BE DEFINED AS A COORDINATED SET OF RULES AND PROCEDURES

THAT ALLOW FOR ROUTINE DECISIONS SUCH AS: 1. WHEN IT IS NECESSARY TO PLACE AN ORDER ( OR SET UP PRODUCTION ) TO REPLENISH

INVENTORY? 2. HOW MUCH IS TO BE ORDERED (OR PRODUCED ) FOR EACH REPLENISHMENT? REGARDLESS OF ITEMS HELD IN STOCK, AN INVENTORY MANAGEMENT SYSTEM CAN BE VIEWED

AS BEING STRUCTURED OF FOLLOWING SUB SYSTEMS:

1. ACCOUNTING FOR INVENTORIES: IT CONCERNS WITH THE CAREFUL RECORD KEEPING OF INVENTORY CONTROL-NAMELY, DELIVERY LEAD TIMES, SOURCE OF ACQUISITION, ORDERING RESTRICTIONS, DATES OF ITEMS RECEIVED OR ISSUED ETC.FOR VARIOUS PRACTICAL OR FINANCIAL REASONS, ACCOUNTING METHODS SUCH AS FIFO AND LIFO MAY BE EMPLOYED.

2. DECISION RULES: THESE ARE MAINLY PLANNING ( WHAT TO STORE; WHERE ARE THE BEST SOURCE FOR PROCUREMENT ) AND CONTROL ( WHEN TO ORDER AND HOW MUCH TO ORDER).

3. OPERATING CONSTRAINTS: THESE CONSTRAINTS BRING THE DECISION RULES TOGETHER WITH OPTIMAL INVENTORY POLICIES.

4. SYSTEM’S MEASURE OF PERFORMANCE: THIS IS DIRECTLY RELATED TO THE TOTAL MIMINMUM INVENTORY COST NECESSARY TO SATISFY FORECASTED DEMAND.

• INVENTORY CONTROL TERMINOLOGY• I. INVENTORY RELATED COSTS ( ECONOMIC PARAMAETERS):• A] PURCHASE ( OR PRODUCTION ) COSTS: BECOMES IMPORTANT WHEN QUANTITY

DISCOUNTS OR PRICE BREAKS CAN BE SECURED FOR PURCHASES ABOVE CERTAIN QUANTITY OR WHEN ECONOMIES OF SCALE SUGGEST THAT THE PER UNIT PRODUCTION CAN BE REDUCED BY A LARGER PRODUCTION RUN.

• B] ORDERING ( OR SET UP ) COSTS : THIS INCLUDE ADMINISTRATIVE, TRANSPORTATION, RECEIVING AND INSPECTION OF GOODS ETC.

• C] CARRYING ( OR HOLDING ) COSTS: THESE COSTS ARE ASSOCIATED WITH HOLDING A GIVEN LEVEL OF INVENTORY ON ONE HAND, AND VARY WITH THE LEVEL AND LENGTH OF TIME INVENTORY IS HELD. IT CONSISTS OF ALL THOSE COSTS THAT ARE INCURRED DUE TO COST OF MONEY INVESTED IN INVENTORY, STORAGE COST, INSURANCE, DEPRECIATION, TAXES ETC.

• THIS COST MAY ALSO BE EXPRESSED AS A PERCENTAGE OF AVERAGE RUPEE VALUE OF INVENTORY HELD RATHER THAN SOME SPECIFIED RUPEE CARRYING COST PER UNIT HELD. THE VARIABLES FOR THE CARRYING COST PORTION ARE AS FOLLOWS:

• I = AVERAGE AMOUNT OF INVENTORY HELD PER UNIT TIME AS A PERCENTAGE OF AVERAGE RUPEE VALUE OF INVENTORY.

• P = PRICE ( OR VALUE ) OF HOLDING ONE UNIT PER UNIT TIME.• THEREFORE THE TOTAL CARRYING COST MAY NOW BE EXPRESSED AS ; CARRYING COST = I X P• D] SHORTAGE ( OR STOCK OUT ) COSTS: THESE ARE THE PENALTY COSTS ASSOCIATED WITH

EITHER A DELAY IN MEETING THE DEMAND OR INABILITY TO MEET IT AT ALL DUE TO SHORTAGE OF STOCK.

• THE OPTIMAL INVENTORY POLICY IS USUALLY BASED ON, AND IS DETERMINEDFROM, THE ABOVE DISCUSSED FOUR CATEGORIES OF COSTS AND THEIR RELATIONSHIP TO DIFFERENT INVENTORY LEVELS.

2. DEMAND : CUSTOMER’S DEMAND, THAT IS , SIZE OF DEMAND, RATE OF DEMAND AND THE PATTERN OF DEMAND FOR A GIVEN TIME IS EXTREMELY IMPORTANT IN THE DETERMINATION OF AN OPTIMAL INVENTORY POLICY. IT CAN EITHER BE DETERMINISTIC OR PROBABILISTIC.

3. ORDER CYCLE : THE TIME PERIOD BETWEEN PLACEMENT OF TWO SUCCESSIVE ORDERS IS REFERRED TO AS AN ORDER CYCLE. THE ORDER MAY BE PLACED ON THE BASIS OF FOLLOWING TWO TYPES OF INVENTORY REVIEW SYSTEM:

a] FIXED ORDER QUANTITY SYSTEM OR THE RE-ORDER POINT SYSTEM, IN WHICH A LEVEL CALLED THE RE-ORDER LEVEL IS DETERMINED. AS SOON AS THE STOCK LEVEL REACHES THIS POINT, AN ORDER FOR A PREDETREMINED NUMBER OF UNITS IS PLACED.

b] PERIODIC REVIEW SYSTEM, WHERE THE INVENTORIES ARE REPLENISHNED AT FIXED INTERVALS OF TIME. WHEREAS THE SIZE OF ORDER IS FIXED IN PREVIOUS SYSTEM AND THE TIME IS NOT, IN THIS SYSTEM THE TIME AFTER WHICH THE SUPPLIES ARE ORDERED IS FIXED BUT NOT THE QUANTITY TO BE ORDERED.

4. TIME HORIZON : THE PERIOD OVER WHICH THE INVENTORY LEVEL WILL BE CONTROLLED IS REFERRED TO AS TIME HORIZON.

5. LEAD TIME: THE TIME BETWEEN ORDERING A REPLENISHMENT OF AN ITEM AND ACTUALLY RECEIVING THE ITEM INTO INVENTORY IS REFERRED TO AS LEAD TIME. THE LEAD TIME CAN BE EITHER DETERMINISIC, CONSTANT OR VARIABLE, OR PROBABILISTIC. IF THE LEAD TIME IS ZERO,THEN WE HAVE THE SPECIAL CASE OF INSTANTANEOUS DELIVERY; i.e. NO NEED OF PLACING AN ORDER IN ADVANCE. IF THE LEAD TIME EXISTS AND ALSO DEMAND KNOWN, THEN IT IS REQUIRED TO PLACE AN ORDER IN ADVANCE BY AN AMOUNT OF TIME EQUAL TO LEAD TIME.

• FIXED ORDER QUANITY SYSTEMS• THE FIXED-ORDER QUANTITY SYSTEM OF INVENTORY MANAGEMENT IS ALSO CALLED THE Q-

SYSTEM. THIS PLACES ORDER FOR THE SAME QUANTITY OF A MATERIAL EACH TIME THAT MATERIAL IS OREDRED.HOWEVER, WHEN THE ORDER IS PLACED IS ALLOWED TO VARY. INVENTORIES FALLS UNTIL A CRITICAL INVENTORY LEVEL , THE ORDER POINT, TRIGGERS AN ORDER.THE ORDER POINT IS DETERMINED BY ESTIMATING HOW MUCH WE EXPECT TO USE OF A MATERIAL BETWEEN THE TIME WE ORDER AND RECEIVE ANOTHER BATCH OF THAT MATERIAL. WHEN THE BATCH IS RECEIVED AND INVENTORY IS REPLENISHED, THE FIXED ORDER QUANTITY IS PLACED IN INVENTORY.

• THE TWO BIN CONTROL OF INVENTORY CONTRL IS A SIMPLE APPLICATION OF THIS TYPE OF SYSTEM. TWO DECISIONS ARE ESSENTIAL TO FIXED ORDER QUANTITY SYSTEMS : ORDER QUANTITIES AND ORDER POINTS.

• DETERMINING ORDER QUANTITIES

WE DEVELOP HERE ESTIMATES OF OPTIMAL ORDER QUANTITIES FOR THREE INVENTORY MODELS:

• MODEL -1 : BASIC ECONOMIC ORDER QUANTITY MODEL• THIS IS MOST ELEMENTARY OF ALL MODELS AND ALSO KNOWN AS THE WILSON

FORMULATION. THE OBJECTIVE OF THE STUDY OF THIS MODEL IS TO DETERMINE AN OPTIMUM ORDER QUANTITY (EOQ) SUCH THAT THE TOTAL INVENTORY COST IS MINIMIZED. WE ILLUSTRATE THIS MODEL AFTER MAKING THE FOLLOWING ASSUMPTIONS .

• ASSUMPTIONS :

• 1. ANNUAL DEMAND,CARRYING COST, AND ORDERING COST FOR A MATERIAL CAN BE ESTIMATED.

• 2. AVERAGE INVENTORY LEVEL FOR A MATERIALIS ORDER QUANTITY DIVIDED BY 2 i.e. Q /2. THIS IMPLICITY ASSUMES THAT NO SAFETY STOCK IS UTILIZED, ORDERS ARE RECEIVED ALL AT ONCE, MATERIALS ARE USED AT UNIFORM RATE , AND MATERIALS ARE ENTIRELY USED UP WHEN THE NEXT ORDER ARRIVES.

• 3. STOCKOUT, CUSTOMER RESPONSIVENESS, AND OTHER COSTS ARE INCONSEQUENTIAL.• 4. QUANTITY DISCOUNTS DO NOT EXIST.

• VARIABLE DEFINITIONS :

• Q = NUMBER OF UNITS ( OR QUANTITY ) ORDERED ( SUPPLIED) PER ORDER ( UNITS/ORDER )• D = DEMAND IN UNITS ( USAGE) OF INVENTORY PER YEAR ( UNITS/ YEAR)• N = NUMBER OF ORDERS PLACED PER YEAR• TC = TOTAL INVENTORY COST ( Rs./ YEAR )• Co = ORDERING COST PER ORDER PLACED ( Rs. /ORDER)• Ch = CARRYING OR HOLDING COST PER UNIT PER PERIOD OF TIME THE INVENTORY IS HELD

( Rs./UNIT)

Cs = SHORTAGE COST, PER UNIT OF INVENTORY OR EXPRESSED AS A PERCENTAGE OF AVERAGE RUPEE VALUE OF INVENTORY.

• R = REORDER POINT UNITS• L = LEAD TIME ( WEEKS OR MONTHS )• t = REORDER CYCLE ( THE ELEPSED TIME BETWEEN PLACEMENT OF TWO ORDERS MEASURED AS

A FRACTIONAL PART OF THE STANDARD TIME PERIOD )

• COST FORMULAS:

1. ANNUAL ORDERING COST = NUMBER OF ORDERS PER YEAR X ORDERING COST PER ORDER = N X Co = TOTAL ANNUAL DEMAND / QUANTITY ORDERED EACH TIME X Co = D/Q X Co2. ANNUAL CARRYING COST = AVERAGE UNITS IN INVENTORY X CARRYING COST PER UNIT = Q/2 X Ch

THE TOTAL INVENTORY COST THEN, IS THE SUM OF THESE TWO COSTS: TC = D/Q X Co + Q/2 X Ch

THE TOTAL COST IS MINIMUM AT A POINT WHERE ORDERING COST EQUAL CARRYING COSTS. THUS , ECONOMIC ORDER QUANTITY OCCURS AT APOINT WHERE : ORDERING COST = CARRYING COST

THEREFORE, D/Q X Co = Q/2 X Ch Q² = 2DCo / Ch THUS OPTIMAL Q ( EOQ ) IS DERIVED TO BE Q ( EOQ) = √2 DCo/ Ch

• MODEL – 2 EOQ FOR PRODUCTION LOTS

• THIS MODEL IS USEFUL FOR DETRMINING THE SIZE OF ORDERS IF A MATERIAL IS PRODUCED AT ONE STAGE OF PRODUCTION, STORED IN INVENTORY , AND THEN SENT ALONG TO NEXT STAGE IN PRODUCTION OR SHIPPED TO CUSTOMERS.

• THIS MODEL HAS ONLY ONE SLIGHT MODIFICATION TO MODEL 1 : ORDERS ARE ASSUMED TO BE SUPPLIED OR PRODUCED AT A UNIFORM RATE RATHER THAN ALL AT ONCE .

• ASSUMPTIONS:

• 1. ANNUAL DEMAND,CARRYING COST, AND ORDERING COST FOR A MATERIAL CAN BE ESTIMATED.

• 2. NO SAFETY STOCK IS UTILIZED, MATERIALS ARE SUPPLIED AT UNIFORM RATE ( p) , AND USED AT A UNIFORM ARTE ( d ), AND MATERIALS ARE ENTIRELY USED UP WHEN THE NEXT ORDER BEGINS TO ARRIVE.

• 3. STOCKOUT, CUSTOMER RESPONSIVENESS, AND OTHER COSTS ARE INCONSEQUENTIAL.• 4. QUANTITY DISCOUNTS DO NOT EXIST• 5. SUPPLY RATE ( p ) IS GREATER THAN USAGE RTAE ( d).

• VARIABLE DEFINITIONS :• • ALL THE DEFINITIONS IN MODEL 1 APPLY ALSO TO MODEL 2. ADDITIONALLY:

• d = RATE AT WHICH UNITS ARE USED OUT OF INVENTORY ( UNITS PER TIME PERIOD )

• P = RATE AT WHICH UNITS ARE SUPPLIED TO INVENTORY ( SAME UNITS AS d )

COST FORMULAS: MAXIMUM INVENTORY LEVEL = INVENTORY BUILD UP RATE X PERIOD OF INVENTORY = ( p – d ) ( Q /p ) MINIMUM INVENTORY LEVEL = 0 AVERAGE INVENTORY LEVEL = ½ { ( p – d ) ( Q / p ) + 0 } = ( Q/2) [ ( p – d ) /p ] ANNUAL CARRYING COST = AVERAGE INVENTORY LEVEL X CARRYING COST = ( Q/2) [ ( p – d ) /p ] Ch. ANNUAL ORDERING COST = NUMBER OF ORDERS PER YEAR X ORDERING COST PER ORDER

= N X Co = TOTAL ANNUAL DEMAND / QUANTITY ORDERED EACH TIME X Co = ( D/Q )Co THE TOTAL INVENTORY COST THEN, IS THE SUM OF THESE TWO COSTS: TC = (D/Q ) Co + ( Q/2) [ ( p – d ) /p ] Ch THE TOTAL COST IS MINIMUM AT A POINT WHERE ORDERING COST EQUAL CARRYING COSTS. THUS , ECONOMIC ORDER QUANTITY OCCURS AT APOINT WHERE : ORDERING COST = CARRYING COST THEREFORE, ( D/Q )Co = ( Q/2) [ ( p – d ) /p ] Ch Q² =( 2 D Co /Ch) [ p/ ( p-d )} Q ( EOQ ) =√ ( 2 D Co /Ch) [ p/ ( p-d )}

MODEL -3 EOQ WITH QUANTITY DISCOUNTSASSUMPTIONS : 1. ANNUAL DEMAND,CARRYING COST, AND ORDERING COST FOR A MATERIAL CAN BE ESTIMATED.2. AVERAGE INVENTORY LEVEL CAN BE ESTIMATED AT EITHER : Q/2 – IF THE ASSUMPTIONS OF MODEL 1 PREVAIL. Q/2 [ ( p-d ) /p ] – IF THE ASSUMPTIONS OF MODEL 2 PREVAIL.3. STOCKOUT, CUSTOMER RESPONSIVENESS, AND OTHER COSTS ARE INCONSEQUENTIAL.4. QUANTITY DISCOUNTS DO EXIST. AS LARGER QUANTITIES ARE ORDERED, PRICE BREAKS APPLY TO ALL

UNITS ORDERED.VARIABLE DEFINITIONS :ALL THE DEFINITIONS IN PREVIOUS MODELS APPLY TO MODEL 3. ADDITTIONALLY: TMC = TOTAL ANNUAL MATERIAL COST ac = ACQUISTION COST OF EITHER PURCAHSING OR PRODUCING ONE UNIT OF A

MATERIAL ( Rs. PER UNIT )FORMULAS :THE EOQ AND TC FORMULA FROM EITHER MODEL 1 OR MODEL 2 ARE APPLIED TO MODEL 3, DEPENDING

ON ASSUMPTIONS BEST FIE THE INVENTORY SITUATION.ANNUAL ACQUISTION COST = ANNUAL DEMAND X ACQUISTION COST = ( D ) ac TOTAL ANNUAL MATERIALS COST (TMC ) = TOTAL ANNUAL STOCKING COST +

ANNUAL ACQUISTION COST = TC + ( D ) ac

• DETERMINING ORDER POINTS• FOR SETTING ORDER POINTS IN A FIXED ORDER QUANTITY INVENTORY SYSTEM,OPERATIONS

MANAGERS ARE CONFRONTED WITH AN UNCERTAIN DEMAND DURING LEAD TIME. • DEMAND DURING LEAD TIME ( DDLT) MEANS THE AMOUNT OF A MATERIAL THAT WILL BE DEMANDED

WHILE WE ARE WAITING FOR AN ORDER OF A MATERIAL TO ARRIVE AND REPLENISH INVENTORY.

• IF ORDERS ARRIVE LATE OR IF DEMAND FOR THE MATERIALS IS GREATER THAN EXPECTED WHILE WE ARE WAITING FOR AN ORDER TO COME IN, A STOCKOUT CAN OCCUR.

• A STOCKOUT MEANS THAT THERE IS INSUFFICIENT INVENTORY TO COVER DEMANDS FOR A MATERIAL DURING LEAD TIME.

• SO TO AVOID STOCK OUT A SAFETY STOCK IS CARRIED OUT. BUT IF WE CARRY TOO MUCH SAFETY STOCK, THE COST OF CARRYING THESE MATERIALS BECOMES EXCESSIVE, HOWEVER , WHEN TOO LITTLE SAFETY STOCK IS CARRIED , THE COST OF STOCKOUTS BECOMES EXCESSIVE. SO OPERATIONS MANAGERS WANT TO BALANCE BETWEEN THESE TWO COSTS AS THEY SET ORDER POINTS.

• • ORDER POINT = EXPECTED DEMAND DURING LEAD TIME + SFATEY STOCK. • OP = EDDLT + SS• IN ATTEMTING TO BALANCE THE COSTS OF CARRYING TOO MUCH OR TOO LITTLE SAFETY STOCK, AN

OPTIMAL SOLUTION TO PROBLEM IS SEARCHED. THE MAIN OBSTACLE TO DETERMINING OPTIMAL SAFETY STOCK LEVELS IS ESTIMATING THE COSTS OF STOCKOUTS. TO OVERCOME THE DIFFICULTY IN ACCURATELY DETERMINING THE COST OF STOCKOUTS, ANALYSTS HAVE TAKEN ANOTHER APPROACH TO SETTING SAFETY STOCKS- STTTING ORDER POINTS AT SERVICE LEVELS.

• SERVICE LEVEL REFERS TO THE PROBABILITY THST A STOCKOUT WILL NOT OCCUR DURING LEAD TIME.